On Maximal and Minimal Solutions for Set-Valued Differential Equations with Feedback Control

Abstract

In this paper, we present the existence of extremal solutions of set-valued differential equations with feedback control on semilinear Hausdorff space under Hukuhara derivative which is developed under the form $D_{H}X\left(t\right)=F\left(t,X\left(t\right),H(t,X(t))\right)$, $X(0)=X_0$, for all $t\in \left[0,T\right]$ with the monotone iterative technique and we will verify that monotone sequence of approximate solutions converging uniformly to the solution of the problem, that is useful for optimization problems.